Personally, I am very interested in trying to understanding “cause and effect”.One dataset I haven’t stumbled across is a detailed [i.e. km specific] Sun-Earth distance ephemeris – similar to the Earth-Moon apogee-perigee distance tables.

This level of detail should clearly show the Earth distance varying [in step with the Lunar cycle] as the Earth rotates around the Earth-Moon barycentre.

Therefore, I think it is really interesting [important] to clearly demonstrate that the TSI “lunar signature” is related to the Earth’s distance from the Sun because there are other possibilities like:
Increased solar wind penetration into the atmosphere at Full Moon.
And/Or
Increased Zodiacal Light at Full Moon.

Question: Have you been able to specifically pin down the Sun-Earth distance?

Another of my outstanding “dig here” queries relates to the concept of the Solar System Barycentre [SSB] which should also affect Sun-Earth distance and TSI.

Question: Have you found any detectable SSB signal in the raw TSI data?